# Good Sets

Given an integer $$n\geq2$$, suppose that there are $$mn$$ points on a circle. We paint the points in $$n$$ different colours so that there are $$m$$ points of each colour. Determine the least value of $$M$$ with the following property: for each $$m\geq M$$, given any such colouring of the $$mn$$ points, there exists a set of $$n$$ points that contains one point of each colour, and with no two adjacent.

×